smc

Question

A regular hexagon with sides of length 6 has an isosceles triangle attached to each side. Each of these triangles has two sides of length 8. The isosceles triangles are folded to make a pyramid with the hexagon as the base of the pyramid. What is the volume of the pyramid?

Accepted Answer

The distance from a corner to the center is 6, and from the corner to the top of the pyramid is 8, so the height is 8^2 - 6^2 = 64 - 36 = 28 = 27. The area of the hexagon is 332 (side)^2 = 332 6^2 = 543 Thus, the volume of the pyramid is 13 base height = 543 273 = 3621.